Is the formula of the angular momentum conservation wrong?

[Fletcher]

Fletcher's Wheel Decoder :

As applies to COAM, & Weight & Balance/Law of Levers, for rotational motion of mass (with inertia) about an axis or fulcrum.

Gravity OFF for CoAM; ON for dual masses about a fulcrum.

[Furcurequs]

zoelra,

Sorry I didn't get back to you sooner.

I agree with your fundamental argument. I thought it was important, though, that we try to get the terminology correct. I also thought it would be good for people to think about the forces involved so as to perhaps better understand why the angular momentum of the moving mass is not conserved when the string wraps around the pole.

The before and after conditions that you used, of course, show that to be the case.

The force from the string on the moving mass has a component that is at right angles to the moment arm from the center of the pole. The total force of acceleration on the moving mass, then, is such to change the direction of motion of the moving mass and its angular momentum without changing its speed.

Likewise there is a torque on the pole, since the string is pulling at a tangent to the rim rather than through the center of the pole as it would do with circular motion.

So, there's an exchange of angular momentum with the pole and earth or whatever it is attached to.

There would, of course, also be an exchange of linear momentum if one wanted to consider that little detail.

Here is a drawing I did in which I have hopefully shown the relevant information. By convention, the angular momentum pseudovector would be pointed into the screen the way I've drawn it with a clockwise motion.



Dwayne

[zoelra]

Thanks Dwayne and good work.

[Fletcher]

I want to go back to basics for a moment & make some points for consideration.

In Wubbly's spreadsheet analysis of the battery & hangar experiment he posted the results of incremental decreases in the radial distance the mass was moved inwards [2r to 1r] with energy inputted into the system (see attachment).

This gave a spiral path [to the observer] to 1r [as the sim showed] - this was because considerable energy [integral of force x dispalcement] was required to make the mass transition occur against Cf's - & that meant the mass was accelerated [along the radial length] & then decelerated at the 1r position - this deceleration would happen abruptly with impact against a stop - Wubbly's ideal calculations showed the very best situation where there was no 'wasted' energy of inwards impact against a stop - so a large force could be applied for a short time then let the mass coast inwards due inertia & gently touch the stop - that would be the most energy efficient method of transitioning the mass from 2r to 1r.

This showed that the mass v & mv doubled at 1r [1/2 radius change] & KE quadrupled; the rpm also quadrupled - COAM proven when looking at the rotational cross checks in his spreadsheet.

I then took Wubbly's inwards calculating spreadsheet & reversed it for the outwards moving situation where mass moves from 1r to 2r - this showed a reversal process [taken in incremental steps] which ultimately ended up with the mass having 1/2 v & mv, & 1/4 KE, with rpm 1/4 - the sim showed not a spiral track outwards but a straight line path (tangential) & this was because Cf's or inertia or momentum carried the mass outwards & the v & mv was not depleted while transitioning [i.e. maintains it speed], until impact with the rim stop at 2r.

The point being that the reversal of the spreadsheet in incremental steps was not technically correct - it showed a constant slowing down of the transitioning mass, which is not the case as explained above.

...........................

We know that a mass at 2r is 4 times as hard to move [rotational inertia, or moment of inertia] that one at 1r - which comes first i.e. the fundamental principle [MOI or KE ?] & which is the correct discription of what actually happens ?

1. the v & mv was halved, & rpm & KE dropped to a 1/4 because of rotational inertia of moving a mass at 2r (I = mr^2) ?

OR ...

2. the v & mv was halved, & rpm & KE dropped to a 1/4 because the mass lost so much KE [i.e. lost 3/4's of its energy] on impact at right angles to the radial against a perpendicular rim ?

.............................

We know the mass will transition outwards at the release speed [constant speed of transition] - we know it will lose 3/4's its KE when it impacts the rim stop [the abrupt halt].

We know we could place a spring between the mass & the rim stop & have the mass compress it storing all of the 3/4's KE it would lose otherwise.

Since we can store this energy we can use it again.

If we use the stored energy to drive the wheel forward via mechanical linkages to a grounded stator [for example] so that the wheel has a greater rpm, then the mass would have a higher v & mv, plus KE whilst at 2r & higher than CoAM would predict.

N.B. using the excess KE to create torque at the axis is one method, another is to use a pin at the rim that fires rapidly & impacts against an external block for example [force applied at 2r], that increases rpm etc - these are just hypothetical examples.

ETA: using todays technology say, we could have the mass push a rod thru a solenoid generating current (or a steel mass passing thru a coil; Lenz effect slows the mass) - that current could then heat a shape memory metal like nitanol on the stator which straightens & pushes the wheel forward [like a ratchet], as an example.

OR .. we could use a piston activated by pneumatics or hydraulics, to push against the stator or an external block near the rim - the piston having a spring return etc.

Is this a violation of CoAM ?

[Furcurequs]

Fletcher,

If you use the stored energy to apply forces to a stator to increase the rotational speed, those forces would not be directed through the center of rotation and so there would be a torque on the rotating part of the system. For angular momentum to be conserved in this case, then, we would need to consider the larger system that also includes the mass being pushed against.

Dwayne

[cloud camper]

It is possible to arrange the swinging or sliding weights in different configurations of course to alter the effects.

One configuration is to hinge the weights arms at the rim so that the weights follow a straighter (non spiral) path to the rim (swinging backwards relative to the rim direction).

This maximizes impact force since the weights do not have to be accelerated along the spiral path. A sizable impact can then be effected at 90 degrees to the rim BUT now we have the weight moving at near zero velocity relative to an external observer while the rim speeds on.

This requires much more work to accelerate the weight back to rim speed.

Another configuration is to hinge the weights at the rim so that the swing is in the same direction of the rim rotation.

This accelerates the weights to the same speed as the rim but of course
slows the rim conserving total AM.

One could also arrange the weights to impact the rim to increase rim speed but we can't forget that the equal and opposite reaction is to reduce
or even reverse velocity of the impacted weights. This is not desirable!

So we have a case of pay me now or pay me later.

[Furcurequs]

I then took Wubbly's inwards calculating spreadsheet & reversed it for the outwards moving situation where mass moves from 1r to 2r - this showed a reversal process [taken in incremental steps] which ultimately ended up with the mass having 1/2 v & mv, & 1/4 KE, with rpm 1/4 - the sim showed not a spiral track outwards but a straight line path (tangential) & this was because Cf's or inertia or momentum carried the mass outwards & the v & mv was not depleted while transitioning [i.e. maintains it speed], until impact with the rim stop at 2r.

The point being that the reversal of the spreadsheet in incremental steps was not technically correct - it showed a constant slowing down of the transitioning mass, which is not the case as explained above.

If the masses weren't suddenly released but rather moved radially outward against a controlled resistance, it could be reversible in regards to the kinetic energy and the spiraling outwards. The energy that was lost at the rim in your simulation, then, in such a case would be gradually taken away as the mass does work against the resistance.

It would be like the spinning skater slowly letting her arms move back outwards while resisting the centrifugal reactive forces on them. The energy from the work she did to increase the speed of her rotation initially when pulling her arms inwards would then just do work on her muscles as she let her arms back out.

Dwayne

[Fletcher]

Thanks Dwayne & CC for your thoughtful comments !

If the masses weren't suddenly released but rather moved radially outward against a controlled resistance, it could be reversible in regards to the kinetic energy and the spiraling outwards [FT: would ocurr, rather than the straight line track we see]. The energy that was lost at the rim in your simulation, then, in such a case would be gradually taken away as the mass does work against the resistance.

It would be like the spinning skater slowly letting her arms move back outwards while resisting the centrifugal reactive forces on them. The energy from the work she did to increase the speed of her rotation initially when pulling her arms inwards would then just do work on her muscles as she let her arms back out.

Dwayne

Yes, using a variable resistive dampener [like an oil filled shock absorber] for instance would take away that KE - we would lose all that energy to frictions & heat - and the track outwards would be a spiral shape instead of the straight line track we see - in that case the symmetry would be absolute for inwards & outwards movement of masses - as it stands I am saying that whilst the end result is the same because the tracks are different from (the perspective of an observer) then the symmetry is not a mirror or reverse image - this is important & I'll explain shortly.

Fletcher,

If you use the stored energy to apply forces to a stator to increase the rotational speed, those forces would not be directed through the center of rotation and so there would be a torque on the rotating part of the system. For angular momentum to be conserved in this case, then, we would need to consider the larger system that also includes the mass being pushed against.

Dwayne

I agree Dwayne - the CoAM LAW states that the axis must be fixed & there must be no external input of torque - I have argued that we have just redirected system energy & not added any additional energy or torque.

The case is made that to have a consistent CoAM LAW we have to widen the net to include the earth grounding - that seems logical & proper - then we can accept that the rim speed can be increased by force redirection.

BUT ... that is not all !

I have an All Blacks game to watch shortly - later today I will put up the math [in simple form, with pics ; everyone should be able to follow it] that to my mind proves that there is indeed 'An Elephant In The Room', & show the possibility of something extraordinary for those that can visualize it !

I'll probably post it on my thread, http://www.besslerwheel.com/forum/viewt ... 097#129097 , because this thread is predominantly about CoAM, though there is obvious overlap.